I found this PowerPoint presentation wherein it defines a "successful" balloon aortic valvuloplasty as one in which the "patient did not die." Well, I'd happen to agree. (There are more criteria than that, actually, and the procedure is successful more than 80% of the time, so that's good news.)
Some of this information is a little skewed, though, because they use balloon aortic vavuloplasty for really old people who aren't healthy enough for bypasses or valve replacements, in addition to little kids like Stoic Sam. (For instance, some of the statistics have the patients divided into three groups, under 70, between 70 and 79, and over 80.)
The conclusion of this slide show is that mortality is low but morbidity (prevalence of the condition) is high. But again, they're dealing with old people who need the procedure because of a lifetime of heart health, not because of a birth defect, so I don't know how much of that applies to us.
Here's an article about a successful BAV on a 1,600 gram (3 lbs. 8 oz.) infant. (I might only be able to see this article because I'm on the Internet at a university right now; if this doesn't work for someone else, let me know).
Here's the abstract of an article I can't even get to on the university server about the best method of treating infantile aortic valve stenosis. Their conclusion: punt. (They're trying to make me pay $25 a year so I can read a report that concludes with "it depends"? No wonder doctors are rich!)
Also, it appears that "cutting edge" stuff in this field revolves around doing this to a fetus, which seems even crazier.